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- W3043897899 abstract "Let γ be an open cover of a space X. If there is a metric d on X which metrizes each member of γ, then X is said to be γ-metrizable. This notion was introduced and studied by M.A. Al Shumrani in [20]. We give an example to show that there is a gap in the proof of Theorem 2.1 and we give an example of a regular γ-metrizable space which is not metrizable, showing that main Theorems 2.1 and 2.4 in Al Shumrani's article are false. We discuss some properties of γ-metrizable spaces and get the following conclusions. If Xn is a γn-metrizable space for every n∈N, then the product space X=∏n∈NXn is γ-metrizable for the natural open cover γ of X. If X has a point-finite open cover by semi-stratifiable subspaces of X, then X is semi-stratifiable. Hence X is a semi-stratifiable space if X is a metacompact γ-metrizable space. If X is a regular γ-metrizable space and the family γ is a σ-HCP open cover of X, then X is metrizable. A space X is metrizable if and only if X is a paracompact γ-metrizable space. Every T1-space X with a σ-weakly hereditarily closure-preserving network is a D-space. We finally get that if X is a γ-metrizable space and the family γ is a σ-weakly hereditarily closure-preserving open cover of X, then X is a D-space." @default.
- W3043897899 created "2020-07-29" @default.
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- W3043897899 date "2020-08-01" @default.
- W3043897899 modified "2023-09-24" @default.
- W3043897899 title "A study of γ-metrizable spaces" @default.
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- W3043897899 doi "https://doi.org/10.1016/j.topol.2020.107327" @default.
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